Monetary Policy Design in the Basic New Keynesian Model Jordi Galí CREI, UPF and Barcelona GSE June 216 Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy Design June 216 1 / 12
The Basic New Keynesian Model: Non-Policy Block New Keynesian Phillips Curve π t = βe t {π t+1 } + κ p ỹ t Dynamic IS Equation ỹ t = 1 σ (i t E t {π t+1 } rt n ) + E t {ỹ t+1 } where rt n = ρ σ(1 + ϕ)(1 ρ a ) a t + (1 ρ σ + ϕ z )z t Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy Design June 216 2 / 12
Monetary Policy Design: The Case of an Effi cient Natural Equilibrium Assumption: Optimal Policy Implementation y n t = y e t ỹ t = ; π t = i t = r n t + φ π π t where φ π > 1 (determinacy condition) Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy Design June 216 3 / 12
Monetary Policy Design: Simple Rules Evaluation of Alternative Policies Welfare losses (second order approx.) ( W E β t Ut U n ) t = 1 t= U c C 2 E [ β t (σ + ϕ) ỹt 2 + ɛ ] t= λ π2 t Average unconditional welfare losses: L = (σ + ϕ) var(ỹ t ) + ɛ λ var(π t) Example: i t = ρ + φ π π t + φ y ŷ t Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy Design June 216 4 / 12
Table 4.1 Evaluation of Simple Rules: Taylor Rule Technology Demand 1:5 1:5 5 1:5 1:5 1:5 5 1:5 y :125 1 :125 1 (y) 1:85 2:7 2:25 1:6 :59 :68 :28 :31 (ey) :44 :21 :3 1:23 :59 :68 :28 :31 () :69 :34 :5 1:94 :2 :23 :9 :1 L 1:2 :25 :6 7:98 :1 :13 :2 :2
Monetary Policy Design: The Case of an Ineffi cient Natural Equilibrium Assumption: time-varying y n t y e t The New Keynesian Phillips Curve π t = βe t {π t+1 } + κx t + u t where x t y t y e t and u t κ(y e t y n t ) Dynamic IS Equation x t = 1 σ (i t E t {π t+1 } r e t ) + E t {x t+1 } where r e t ρ + σe t { y e t+1 } + (1 ρ z )z t = r n t Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy Design June 216 5 / 12
The Optimal Monetary Policy Problem min E β t ( π 2 t + ϑx 2 ) t t= subject to: π t = βe t {π t+1 } + κx t + u t where {u t } evolves exogenously according to u t = ρ u u t 1 + ε t In addition: x t = 1 σ (i t E t {π t+1 } rt e ) + E t {x t+1 } Note: utility based criterion requires ϑ = κ ɛ Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy Design June 216 6 / 12
Optimal Monetary Policy under Discretion Each period CB chooses (x t, π t ) to minimize subject to π 2 t + ϑx 2 t π t = κx t + v t where v t βe t {π t+1 } + u t is taken as given. Optimality condition: Equilibrium x t = κ ϑ π t ϑ π t = κ 2 + ϑ(1 βρ u ) u κ t ; x t = κ 2 + ϑ(1 βρ u ) u t i t = r e t + ϑρ u + σκ(1 ρ u ) κ 2 + ϑ(1 βρ u ) u t Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy Design June 216 7 / 12
Optimal Monetary Policy under Discretion Implementation: i t = rt e + ϑρ u + σκ(1 ρ u ) κ 2 + ϑ(1 βρ u ) u t + φ π = rt e + Θ i u t + φ π π t ( π t ) ϑ κ 2 + ϑ(1 βρ u ) u t where Θ i σκ(1 ρ u ) ϑ(φ π ρ u ) κ 2 +ϑ(1 βρ u ) and φ π > 1. Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy Design June 216 8 / 12
Figure 5.1 Discretion vs. Commitment: Responses to a Transitory Cost-Push Shock.3-2.2-4.1-6 -8 discretion commitment 2 4 6 8 1 12 output gap -.1 -.2 2 4 6 8 1 12 inflation.4.3 1.8.6.2.4.1.2 -.1 2 4 6 8 1 12 price level -.2 2 4 6 8 1 12 cost-push shock
Figure 5.2 Discretion vs. Commitment: Responses to a Persistent Cost-Push Shock -2-4 -6-8 discretion commitment.5.4.3.2.1 2 4 6 8 1 12 output gap 2 4 6 8 1 12 inflation 2.5 1 2.8 1.5 1.5.6.4.2 2 4 6 8 1 12 price level -.2 2 4 6 8 1 12 cost-push shock
Optimal Monetary Policy under Commitment State-contingent policy {x t, π t } t= that minimizes E β t ( π 2 t + ϑx 2 ) t t= subject to the sequence of constraints: Lagrangean: [ 1 L = E β t t= 2 Optimality conditions: for t =, 1, 2,...with ξ 1 =, π t = βe t {π t+1 } + κx t + u t ( π 2 t + ϑx 2 t ϑx t κξ t = π t + ξ t ξ t 1 = ] ) + ξt (π t κx t βπ t+1 ) Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy Design June 216 9 / 12
Optimal Monetary Policy under Commitment Eliminating multipliers: x = κ ϑ π x t = x t 1 κ ϑ π t for t = 1, 2, 3,... Alternative representation: x t = κ ϑ p t for t =, 1, 2,...where p t p t p 1 Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy Design June 216 1 / 12
Optimal Monetary Policy under Commitment Equilibrium for t =, 1, 2,...where γ Stationary solution: p t = γ p t 1 + γβe t { p t+1 } + γu t ϑ ϑ(1+β)+κ 2 p t = δ p t 1 + δ 1 δβρ u u t for t =, 1, 2,...where δ 1 1 4βγ 2 2γβ (, 1). for t = 1, 2, 3,..., and price level targeting! x t = δx t 1 κδ ϑ(1 δβρ u ) u t κδ x = ϑ(1 δβρ u ) u Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy Design June 216 11 / 12
Optimal Monetary Policy under Commitment Discussion: Gains from Commitment π t = κx t + κ k=1 β k E t {x t+k } + 1 1 βρ u u t Implementation (ρ u = case) for any φ p >. ( ( i t = rt e φ p + (1 δ) 1 σκ )) t α x δ k+1 u t k + φ p p t k= Jordi Galí (CREI, UPF and Barcelona GSE) Monetary Policy Design June 216 12 / 12
Figure 5.1 Discretion vs. Commitment: Responses to a Transitory Cost-Push Shock.3-2.2-4.1-6 -8 discretion commitment 2 4 6 8 1 12 output gap -.1 -.2 2 4 6 8 1 12 inflation.4.3 1.8.6.2.4.1.2 -.1 2 4 6 8 1 12 price level -.2 2 4 6 8 1 12 cost-push shock
Figure 5.2 Discretion vs. Commitment: Responses to a Persistent Cost-Push Shock -2-4 -6-8 discretion commitment.5.4.3.2.1 2 4 6 8 1 12 output gap 2 4 6 8 1 12 inflation 2.5 1 2.8 1.5 1.5.6.4.2 2 4 6 8 1 12 price level -.2 2 4 6 8 1 12 cost-push shock
Figure 5.3 Discretion vs. Commitment in the Presence of a ZLB 5 5-5 -5-1 -1-15 discretion commitment 2 4 6 8 1 12 output gap -15-2 -25 2 4 6 8 1 12 inflation 6 6 4 4 2 2-2 -4-2 2 4 6 8 1 12 nominal rate -6 2 4 6 8 1 12 natural rate